منابع مشابه
On fractional Tikhonov regularization
It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth, i.e., the approximate solution may lack many details that the desired exact solution might possess. Two different approaches, both referred to as fractional Tikhonov methods have been introduced to remedy this shortcoming. This paper investigates the convergence properties of ...
متن کاملFractional Tikhonov regularization with a nonlinear penalty term
Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix and an error-contaminated data vector (right-hand side). This regularization method replaces the given problem by a penalized least-squares problem. It is well known that Tikhonov regularization in standard form may yield appr...
متن کاملFractional Tikhonov regularization for linear discrete ill- posed problems
Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...
متن کاملTikhonov Regularization
An important issue in quantitative nance is model calibration. The calibration problem is the inverse of the pricing problem. Instead of computing prices in a model with given values for its parameters, one wishes to compute the values of the model parameters that are consistent with observed prices. Now, it is well-known by physicists that such inverse problems are typically ill-posed. So, if ...
متن کاملMulti-Parameter Tikhonov Regularization
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, t...
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ژورنال
عنوان ژورنال: Journal of Inverse and Ill-posed Problems
سال: 2015
ISSN: 0928-0219,1569-3945
DOI: 10.1515/jiip-2014-0050